Mahalanobis &amp; Fisher: Mathematical Statistics as a Global Enterprise

Stigler, Stephen M.

doi:10.1007/s13571-018-0168-z

Cited by 4 publications

(4 citation statements)

References 7 publications

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“…These three papers form cornerstones of most traditional modern undergraduate lecture courses in multivariate analysis. Hard on Hotelling's heels came R A (Sir Ronald) Fisher (1890Fisher ( -1962 in England, with his derivation of the linear discriminant function (Fisher 1936), and P C Mahalanobis (1893-1972 in India, with his squared distance measure between populations, now known universally as Mahalanobis distance (Mahalanobis 1936) (see Stigler (2018) for his relationship with Fisher). Both of these were also published in 1936, surely making this a truly memorable year in the development of the subject.…”

Section: The Year 1936: Hotelling Fisher Mahalanobismentioning

confidence: 99%

Linear algebra and multivariate analysis in statistics: development and interconnections in the twentieth century

Bingham

Krzanowski

2022

British Journal for the History of Mathematics

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The most obvious points of contact between linear and matrix algebra and statistics are in the area of multivariate analysis. We review the way that, as both developed during the last century, the two influenced each other. We illustrate this by examining a number of key areas.We begin with matrix and linear algebra, its emergence in the 19th century, and its eventual penetration into the undergraduate curriculum in the 20th century. We continue with a much longer similar account for multivariate analysis in statistics. We pick out the year 1936 as that of three key developments, by H. Hotelling, R. A. Fisher and P. C. Mahalanobis, and in the early post-war period three more key developments, by M. G. Kendall, M. S. Bartlett and C. R. Rao. We then turn to some special results in linear algebra that we need: Schur complements, and related inversion formulae. We briefly discuss four of the contributors, Fisher and Kendall named above, together with S. S. Wilks and T. W. Anderson. We close with thirteen 'case studies', showing in a range of specific cases how these general algebraic methods have been put to good use and changed the face of statistics.Keywords linear algebra, matrix algebra, multivariate analysis in statistics, multivariate normal distribution, Gaussian Regression Formula, Schur complement, singular values decomposition. Time-lineOur main focus is on the 20th century, though we touch on the 18th and 19th (and of course are influenced by the first part of the 21st). Both authors were born in the 1940s and began publishing in the 1970s. We allow ourselves to use the term 'modern', imprecise and subjective as it is, as being as useful in this context as in general usage. It might be loosely read here as 'within living memory'. For example, we say ( §4.3) of Anderson's 1958 book that we regard it as 'the first of the unambiguously modern textbooks we cite'. We invite readers to form their own views here.see Eisenhart (1961)) helped to motivate the development of matrix algebra and linear programming. A study of the emergence of matrix theory as a subject in its own right, with particular reference to the inter-war years, is given by Brechenmacher (2010).J. W. Gibbs, in his lecture notes at Yale of 1881 and 1884 (published 1901), did much to spread the use of vector methods. An early stimulus for these was Grassmann's Ausdehnungslehre of 1844. Vector methods were championed in the UK by O. Heaviside (to whom we owe, e.g., the use of bold face for vectors). For a good brief account of the struggles between the proponents of vectors and quaternions (W. R. Hamilton, 1843), see the Historical Introduction in (Weatherburn 1921). In a paper written while he was still a student, Fisher applied vector methods to geometry (Fisher 1913). Unfortunately, vector methods were still scorned by some as late as 1937; see e.g. the Preface of (Ramsey, 1937).An insight into the our theme a century earlier is provided by the following passage from (Todhunter 1869) acknowledging input from Cayley (thanks to Steve Stigler for t...

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Section: The Year 1936: Hotelling Fisher Mahalanobismentioning

confidence: 99%

Linear algebra and multivariate analysis in statistics: development and interconnections in the twentieth century

Bingham

Krzanowski

2022

British Journal for the History of Mathematics

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“…We are interested in extending Stigler’s contention that Mahalanobis built locally with aims to contribute on a global scale . He brought the statistical world to India and also India to the world (Stigler 2018, S177). 7 And as we will outline, the mobility of the measure is also a way of examining the social value of the Distance Function.…”

Section: Mobility and Social Value: Similarity Measures Race And Faci...mentioning

confidence: 99%

“… 7. His use of R. A. Fisher was to highlight that the global reach was effective in two ways: to parade the world’s most famous statistician before the new cohort in India and to bring India to attention of the world stage (Stigler 2018). …”

mentioning

confidence: 99%

Artificial Intelligence from Colonial India: Race, Statistics, and Facial Recognition in the Global South

Taylor

Gulson

McDuie‐Ra

2021

Science, Technology, & Human Values

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This article examines the history of a similarity measure—the Mahalanobis Distance Function—and its movement from colonial India into contemporary artificial intelligence technologies, including facial recognition, and its reapplication into postcolonial India. The article identifies how the creation of the Distance Function was connected to the colonial “problem” of caste and ethnic classification for British bureaucracy in 1920-1930s India. This article demonstrates that the Distance Function is a statistical method, originating to make anthropometric caste distinctions in India, that became both a technical standard and a mobile racialized technique, utilized in machine learning applications. The creation of the Distance Function as a measure of “similitude” at a particular period of colonial state-making helped to model wider categories of classification which have proliferated in facial recognition technology. Overall, we highlight how a measurement function that operates in recognition technologies today can be traced across time and space to other racialized contexts.

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“…In recent years, interpolative separable density fitting (ISDF) decomposition [51,52] has achieved great development for compressing the numerical redundancy of the orbital pair product in diverse advanced electronic structure methods, including hybrid DFT calculations [52][53][54][55][56], LR-TDDFT [57], GW [58,59] plus Bethe-Salpeter equation (BSE) [60], density functional perturbation theory (DFPT) [61,62], second-order Møller-Plesset theory (MP2) [63], random phase approximation (RPA) [64,65], and quantum Monte Carlo (QMC) simulations [66] within GTOs, NAOs and plane-wave basis sets. The ISDF algorithm decomposes the transposed Khatri-Rao product [67,68] of the Kohn-Sham orbitals (ϕ and ψ) by the selection of grid points in real space, which can be approximated as…”

Section: Introductionmentioning

confidence: 99%

Low-rank approximations to accelerate hybrid functional enabled real-time time-dependent density functional theory within plane waves

Wan

Jiao

et al. 2023

Electron. Struct.

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Real-time time-dependent density functional theory (RT-TDDFT) is a powerful tool for predicting excited-state dynamics. Herein, we combine the adaptively compressed exchange (ACE) operator with interpolative separable density fitting (ISDF) algorithm to accelerate the hybrid functional calculations in RT-TDDFT (hybrid RT-TDDFT) dynamics simulations for molecular and periodic systems within plane wave basis sets. Under this low-rank representation, we demonstrate that the ACE-ISDF enabled hybrid RT-TDDFT can yield accurate excited-state dynamics, but much faster than conventional calculations. Furthermore, we describe a massively parallel implementation of ACE-ISDF enabled hybrid RT-TDDFT dynamics simulations containing thousands of atoms (1,728 atoms), which can scale up to 3,456 CPU cores on modern heterogeneous supercomputers.

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Mahalanobis & Fisher: Mathematical Statistics as a Global Enterprise

Cited by 4 publications

References 7 publications

Linear algebra and multivariate analysis in statistics: development and interconnections in the twentieth century

Linear algebra and multivariate analysis in statistics: development and interconnections in the twentieth century

Artificial Intelligence from Colonial India: Race, Statistics, and Facial Recognition in the Global South

Low-rank approximations to accelerate hybrid functional enabled real-time time-dependent density functional theory within plane waves

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